Home > Geometry > Equation of a Circle

The radius of the circle is 11.1 cm, the radius CM is perpendicular to the chord LK, and MQ measures 3.4 cm. What is the length of the chord LK?

Answer 1

Theodore Abad

# LK~~15.99cm.#

Note that, #CQ+QM=CM.#

#rArr CQ=CM-QM=11.1-3.4=7.7cm.#

In the Right- #Delta CQK, /_CQK=90^@.#

#:. CK^2=CQ^2+QK^2.#

Here, #CQ=7.7cm, and, CK"=radius="11.1cm.#

#:. 11.1^2=7.7^2+QK^2.#

#:. QK^2=11.1^2-7.7^2=123.21-59.29=63.92.#

#:. QK=sqrt63.92~~7.995cm.#

Since, a radius, #bot-# to a chord bisects the chord, we have,

#LK=2QK~~2xx7.995=15.99cm.#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Wyatt Anderson

To find the length of the chord LK, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Given that CM is perpendicular to LK, MQ = 3.4 cm, and the radius of the circle is 11.1 cm, we can set up the equation:

[ MQ^2 + QK^2 = MK^2 ]

[ 3.4^2 + (11.1 - CK)^2 = 11.1^2 ]

Solve for ( CK ) to find the length of the chord LK.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.